Timeline for Coupled Riccati equations
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 16, 2023 at 13:58 | comment | added | Ali Taghavi | I am sorry for my mistake. misread some thing in the OP: I confused and misread $ax^2+bxy$ by $ax+bxy$. I belive that the two systems are not topological equivalent: The OP system is a Homogenous equation invariant under rescalling But the Lotka Volterra system has a center as wiikipedia indicate to. So a center in the first quadrant is not invariant under rescalling $(x,y)\mapsto (\lambda x, \lambda y)$ | |
| Mar 16, 2023 at 10:38 | comment | added | მამუკა ჯიბლაძე | @AliTaghavi Sorry I tried various substitutions but could not reduce this system to the Lotka-Volterra form. Could you please name explicit substitution which transforms the OP system to the form $dx/dt=\alpha x-\beta xy$, $dy/dt=\delta xy-\gamma y$? | |
| Mar 16, 2023 at 10:11 | comment | added | Ali Taghavi | mathoverflow.net/questions/277481/… | |
| Mar 16, 2023 at 10:11 | comment | added | Ali Taghavi | +1 for your effort on this question. The OP concernes the explicite solution and your answer do that. However a geometric approach could be consideration of a metric compatible to the Lotka Volterra system. as you find in the wikipedia link I provided in my answer the system has a center so one can think to an explicite Riemannian ,metric compatible to the system | |
| Mar 16, 2023 at 8:37 | history | edited | მამუკა ჯიბლაძე | CC BY-SA 4.0 |
simplified
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| Mar 16, 2023 at 8:16 | history | answered | მამუკა ჯიბლაძე | CC BY-SA 4.0 |